Question

The distance of the centres of moon and earth is $D$. The mass of earth is $81$ times the mass of the moon. At what distance from the centre of the earth, the gravitational force on a particle will be zero.

• A. $\frac{4D}{3}$
• B. $\frac{2D}{3}$
• C. $\frac{9D}{10}$
• D. $\frac{D}{2}$

Answer 1

The correct option is C $\frac{9D}{10}$

Let mass of moon be $M$.

So, $M_m=M;M_e=81M$


Let $x$ be the distance to the point where gravitational force will be zero and $m^{\prime }$ be the mass of the particle.

$\therefore F_e=F_m$

$\Rightarrow \frac{G{M}_e{m}^{\prime }}{x^2}=\frac{G{M}_m{m}^{\prime }}{(D-x{)}^2}$

$\Rightarrow \frac{G81M{m}^{\prime }}{x^2}=\frac{GM{m}^{\prime }}{(D-x{)}^2}$

$\Rightarrow 9D-9x=x\Rightarrow x=\frac{9D}{10}$

Hence, option $\left(d\right)$ is the correct choice.